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Monday, February 28, 2011

John Brockman's Edge group puts out a question each year to be answered succinctly by a multitude of cutting-edge scientists/thinkers. The resultant responses (and books) always make for interesting reading. The 2010 question was "Is the internet changing the way you think?" All (~170) sometimes redundant, but also diverse, responses are here (or you can buy the book):

The question of what the internet is doing to the human brain and thought is a fascinating one with a wide spectrum of varying opinions. Mathematics is one of the areas where the collaborative nature of the Web (call it "hive mind," "wisdom of large groups," "crowd-sourcing," or any number of other terms) is already proving its efficacy... of course there can also be such a thing as the "madness of crowds!"
My own view is that the intrinsic social and cognitive power that the internet wields will ultimately bulldoze over any of the potential negative effects that may come along with it. Politically, we may already be seeing the benefits in the deposition of long-entrenched autocracies, by populations (digitally) conjoined and organized for the first time in human history. Time will tell... but it is certainly an interesting era (and possibly even inflection point) to be alive, observing human civilization evolve!

Thursday, February 24, 2011

There are a lot of 'bite-size' books out now that introduce readers to a range of key mathematical ideas without getting too technical or too deep (but not too simplistic either). Thought I'd just mention two of the ones I particularly like for anyone not already familiar with them (feel free to mention your own favorite short intros to mathematics for the non-professional, in the comments section):

Monday, February 21, 2011

...and I learned that the "Butterfly Effect" actually goes all the way back to a Ray Bradbury novel... (since I don't read science fiction, or any fiction for that matter, I never knew that... or, did the notion come to Bradbury from yet someone or something else... who got it from.....?!)

Now, a computer could no doubt be made to generate such a sentence as included therein, but could a computer ever recognize the humor in it???

(... and I ask that, because a recent commentator on NPR, contemplating IBM's "Watson" victory over humans in the "Jeopardy" game show, asked aloud if computers, that can certainly match and exceed human mental capacities, could ever possess a 'sense of humor'!?)

Thursday, February 17, 2011

Here a talk by computer scientist Scott Aaronson, author of the popular blog "Shtetl Optimized," in which he entertainingly addresses P vs. NP, and quantum computing, among other things (...all in 15 minutes):

Wednesday, February 16, 2011

An international team of mathematicians is creating a "periodic table" of 3-, 4-, and 5-dimensional "shapes" composing the Universe:

"As these building block shapes are revealed, the mathematicians will work out the equations that describe each shape and through this, they expect to develop a better understanding of the shapes' geometric properties and how different shapes are related to one another."
creating "...a directory that lists all the geometric building blocks and breaks down each one's properties using relatively simple equations."

" ...a computer modelling programme... should enable the researchers to pinpoint the basic building blocks for these multi-dimensional shapes from a pool of hundreds of millions of shapes...The researchers calculate that there are around 500 million shapes that can be defined algebraically in four dimensions and they anticipate that they will find a few thousand building blocks from which all these shapes are made."

"In our project we are looking for the basic building blocks of shapes. You can think of these basic building blocks as 'atoms', and think of larger shapes as 'molecules.' The next challenge is to understand how properties of the larger shapes depend on the 'atoms' that they are made from. In other words, we want to build a theory of chemistry for shapes," added Dr Coates.

Tuesday, February 8, 2011

"Math-blog" is doing a survey to compile a list of people's 'favorite math books' (using that term broadly). If you have one that comes to mind, go fill out their simple form. The more that take part, the merrier:

Sunday, February 6, 2011

Been tied up with other things lately, but will put up for contemplation this passage from chapter 9 of Michael and Ellen Kaplan's book "Chances Are...," wherein they're discussing the work of Edward Lorenz, chaos theory, and deterministic systems:

"The mathematics of chaotic systems produces the same effect at every scale. Tell me how precise you want to be, and I can introduce my little germ of instability one decimal place further along; it may take a few more repetitions before the whole system's state becomes unpredictable, but the inevitability of chaos remains. The conventional image has the flap of a butterfly's wings in Brazil causing a storm in China, but even this is a needlessly gross impetus. The physicist David Ruelle, a major figure in chaos theory, gives a convincing demonstration that suspending the gravitational effect on our atmosphere of one electron at the limit of the observable universe would take no more than two weeks to make a difference in Earth's weather equivalent to having rain rather than sun during a romantic picnic."

"The fact is, in the era of DNA identification, judges and juries simply cannot avoid getting to grips with the relevant math. Identification hinges on those calculations. There may be no way of avoiding bringing mathematicians into court to explain how the calculations are done. But for that to be effective, those judges and juries need first to learn (and accept) that human intuitions about probabilities are hopelessly unreliable."

There is a lot more information around the Web about the statistics of DNA forensics and common misperceptions (...sometimes by people who should know better).

On a pertinent side-note, I'm currently reading "Chances Are..." by Michael and Ellen Kaplan. It's a slightly older volume (2006), so I probably won't write a full review of it, but I have already read enough to say I'm very much enjoying it (one of the best books I've seen on probabilities for a mass audience), and so recommend it to all who have an interest in the topic. Here's a NY Times review of the volume:

Me...

I'm a number-luvin' primate; hope you are too! ..."Shecky Riemann" is the fanciful pseudonym of a former psychology major and lab-tech (clinical genetics), now cheerleading for mathematics! A product of the 60's he remains proud of his first Presidential vote for George McGovern ;-) ...Cats, cockatoos, & shetland sheepdogs revere him. ...now addicted to pickleball.
Li'l more bio here.

...............................--In partial remembrance of Martin Gardner (1914-2010) who, in the words of mathematician Ronald Graham, “...turned 1000s of children into mathematicians, and 1000s of mathematicians into children.” :-)............................... Rob Gluck